For a series of randomly discounted terms we give an integral
criterion to distinguishbetween almost-sure absolute convergence and divergence
in probability to $\infty$, these being the only possible forms of asymptotic
behavior. This solves the existence problem for a one-dimensional perpetuity
that remains from a 1979 study by Vervaat, and yields a complete
characterization of the existence of distributional fixed points of a random
affine map in dimension one.
Publié le : 2000-06-14
Classification:
Distributional fixed point,
perpetuity,
random affine map,
randomly discounted series,
60H25
@article{1019160331,
author = {Goldie, Charles M. and Maller, Ross A.},
title = {Stability of perpetuities},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 1195-1218},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160331}
}
Goldie, Charles M.; Maller, Ross A. Stability of perpetuities. Ann. Probab., Tome 28 (2000) no. 1, pp. 1195-1218. http://gdmltest.u-ga.fr/item/1019160331/